Advancing hybrid quantum-classical algorithms via mean operators

Hybrid quantum-classical algorithms have been suggested to control the quantum entanglement of many-body systems in noisy intermediate-scale quantum technology, and yet their applicability is limited by the numbers of qubits and quantum operations. Here, we propose a mean-operator theory which overcomes limitations by combining the advantages of hybrid algorithms and standard mean-field theory. We demonstrate that an introduction of a mean operator prepares an entangled target many-body state with a significantly reduced number of quantum operations. We also show that a class of mean operators is expressed as time-evolution operators, which indicates that our theory is directly applicable to quantum simulations with Rydberg atoms and trapped ions.